Can Aha Moments be Fake? Towards Quantifying Decorative and True Thinking in Chain-of-Thought

Large language models can generate long chain-of-thought (CoT) reasoning, yet prior work suggests that CoT can be post-hoc rationalization rather than a faithful reflection of the computation through explicitly designed settings. In this work, we go further and propose a \text{True Thinking Score (TTS)} to quantify the causal contribution of each step in CoT to the model's final prediction in realistic reasoning problems. Across eleven models ranging from 1.5B to 1.1T parameters on common reasoning benchmarks, we find that CoTs often interleave \emph{true-thinking} steps, which causally affect the final answer, with \emph{decorative-thinking} steps, which appear useful but have little causal influence; Such decorative steps remain prevalent even for frontier models: Over 30\% of steps in Kimi-K2.6 are decorative on MATH with TTS $\leq$ 0.005. Furthermore, TTS enables effective CoT pruning: removing 50\% of CoT steps with the lowest TTS can largely maintain the performance. Self-training on these pruned CoTs reduces reasoning length by 66\% while preserving performance on Nemotron3-Nano-30B. Finally, we provide a mechanistic analysis showing that LLMs can be steered in the latent space to engage or disengage with reasoning steps. Overall, our results reveal that frontier LLMs often verbalize reasoning steps that are not causally used, challenging both the efficiency and the trustworthiness of CoT.